Answer
The z coordinate of the center of mass is $~~16~cm$
Work Step by Step
By symmetry, the z coordinate of the center of mass for each of the four standing sides is $\frac{L}{2}$ which is $20~cm$
The z coordinate of the center of mass for the bottom surface of the cube is $0$
Let $m$ be the mass of each surface of the cube.
We can find the z coordinate of the center of mass of the cube:
$z_{com} = \frac{(4)(m)(20)+(m)(0)}{5m} = 16~cm$
The z coordinate of the center of mass is $~~16~cm$.
